A bit of a mystery – tenant still paying rent has moved out?

Maybe use the opportunity to get in some electrical and gas safety checks at depth so you can fully check out the property. I would pay particular attention to the meters and loft space.

A minor point, but you should probably inform your insurance company that the property is empty.

This tenant is not doing you or your house any favours.
There is no shortage of good tenants who will look after your property. Serve a S21 and move on.

Your tenant's stories sound like a pack of lies. I'd begin legal repossession.

Much of your description would be consistent with sub-letting, perhaps to more than one sub-tenant. They would charge a higher rent, paid in cash with no tax, enough to pay your rent and turn a profit. Their income is untraceable - and the sub-tenants would be people who want to stay below the radar. If they used old furniture they could scrap it afterwards.

When I had something similar one clue was my tenant repeatedly used the 24 hours' notice to delay visits to ensure there'd be no evidence of her sub-tenants. The only part that sounds inconsistent is your tenant's offer you can enter at any time. Might she think she can get away with that?

Sub-letting tenants tend to pay on time and cause little trouble because they don't want to attract attention. Have you done regular inspections? Could they have been doing this for some time?

If any of the above rings true then you can't accept the situation. If she's not living there, you'd be in breach of your insurance, and if you have a mortgage you'd breach the agreement. There'd also be the question of whether Right to Rent checks have been conducted.

Serve a section 21 (whilst you still can!) and start planning a refurb. Aim to leave on good terms and say you will arrange the redecoration.

I would recommend taking action now by issuing a Section 21 notice to formally end the tenancy. It seems clear that despite their claims, the tenants have moved out and may not return. Given the state of the property and the uncertainty surrounding their intentions, it's crucial to protect your investment and prepare the property for new tenants promptly. Documenting the condition thoroughly will help support your case for any necessary repairs and cleaning.

As the tenant is living at another property, you don't need an s21. It's no longer their main residence, so it's no longer an AST, it's just a contractual tenancy now. You can skip directly to a possession order.

For an AST the property must be their main and only residence I think - Google will confirm the correct wording.

Your building insurance will require some to be living in the property and notification given if it is empty for over a certain period. I they have been out for 6 weeks already, then it is probably already invalidated and you are probably not covered at the moment.

I am similarly at a loss about why they would do this, but subletting as suggested by one of the other comments is as good as anything I can think of. Perhaps it was the sub-tenants that moved out 6 weeks ago and they haven't let it out again yet. Perhaps they told the sub-tenants to be out when you've visited previously.

Have you checked the loft and the electrics?

If your tenants want to pay for 2 properties until they are in arrears it's actually none of your business. Is the holiday chalet accommodation provided for working at the holiday park? But again not really your business.

"the tenant said that I can go in and check anytime without asking her, using my own key". Get it in writing and ideally witnessed.

Until you have a Deed of Surrender signed and dated it is "their" property until they either leave of their own free will and sign a Deed of Surrender or you serve a s21 and begin the eviction process.